Question Number 7076 by Tawakalitu. last updated on 09/Aug/16 Commented by Yozzii last updated on 09/Aug/16 $$\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)^{\mathrm{1}/\mathrm{3}} =\left\{\sqrt{\mathrm{5}}\left(\mathrm{1}+\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}\right)\right\}^{\mathrm{1}/\mathrm{3}} =\mathrm{5}^{\mathrm{1}/\mathrm{6}} \left(\mathrm{1}+{u}\right)^{\mathrm{1}/\mathrm{3}} \\ $$$${u}=\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}<\mathrm{1}. \\ $$$${Also}\:\left(\mathrm{2}−\sqrt{\mathrm{5}}\right)^{\mathrm{1}/\mathrm{3}} =−\mathrm{5}^{\mathrm{1}/\mathrm{6}}…
Question Number 72608 by aliesam last updated on 30/Oct/19 Answered by mind is power last updated on 30/Oct/19 $$\mathrm{s}\left(\mathrm{x}\right)=\mathrm{n}\Rightarrow\mathrm{x}\in\left[\mathrm{10}^{\mathrm{n}−\mathrm{1}} ,\mathrm{10}^{\mathrm{n}} \left[\right.\right. \\ $$$$\mathrm{s}\left(\mathrm{y}\right)=\mathrm{m}\Rightarrow\mathrm{y}\in\left[\mathrm{10}^{\mathrm{m}−\mathrm{1}} ,\mathrm{10}^{\mathrm{m}} \left[\right.\right.…
Question Number 7075 by Tawakalitu. last updated on 09/Aug/16 $${Find}\:{all}\:{the}\:{solution}\:{for}\:{x}\:{and}\:{y}\:{in}\:{the}\:{equation} \\ $$$$ \\ $$$${x}^{{y}} \:+\:{y}^{{x}} \:=\:\mathrm{17}\:\:\:\:……..\:{equation}\:\left({i}\right) \\ $$$${x}\:+\:{y}\:=\:\mathrm{5}\:\:\:\:\:\:………\:{equation}\:\left({ii}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 138135 by Deepak1298 last updated on 10/Apr/21 $$\left({x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right)=\mathrm{4} \\ $$$${find}\:{x}. \\ $$ Answered by ajfour last updated on 10/Apr/21 $${let}\:{x}=\frac{\mathrm{4}}{{t}} \\…
Question Number 7054 by Tawakalitu. last updated on 08/Aug/16 $${Solve}\:{for}\:{x}\:{in}\:{the}\:{equation}\:{below} \\ $$$${x}^{\mathrm{4}} \:+\:\mathrm{2}{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$ \\ $$ Commented by prakash jain last updated…
Question Number 72593 by TawaTawa last updated on 30/Oct/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:\:\mathrm{25\%}\:\mathrm{while}\:\mathrm{its} \\ $$$$\mathrm{width}\:\mathrm{is}\:\mathrm{decrease}\:\mathrm{by}\:\:\:\mathrm{15\%}\:\:\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{rectangle}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square} \\ $$ Answered by Tanmay chaudhury last updated on…
Question Number 138123 by Caroline last updated on 10/Apr/21 Answered by Dwaipayan Shikari last updated on 10/Apr/21 $${Det}\left({M}\right)=\mathrm{0} \\ $$$$\Rightarrow−\mathrm{1}\left(\mathrm{8}−\mathrm{20}\right)−\mathrm{4}\left(\mathrm{8}+\mathrm{60}+\mathrm{4}{k}\right)−\mathrm{4}\left(−\mathrm{4}−\mathrm{75}−\mathrm{5}{k}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{12}−\mathrm{272}−\mathrm{16}{k}+\mathrm{316}+\mathrm{20}{k}=\mathrm{0}\Rightarrow\mathrm{4}{k}=−\mathrm{56}\Rightarrow{k}=−\mathrm{14} \\ $$ Commented…
Question Number 138096 by mr W last updated on 10/Apr/21 $${solve} \\ $$$$\mathrm{2}^{{x}} +\mathrm{4}^{{x}} =\mathrm{8}^{{x}} \\ $$ Commented by MJS_new last updated on 10/Apr/21 $$\mathrm{the}\:\mathrm{complex}\:\mathrm{solutions}\:\mathrm{are}…
Question Number 7021 by FilupSmith last updated on 06/Aug/16 $${z}=\int_{\mathrm{0}} ^{\:{t}} {i}\left(−\mathrm{1}\right)^{{x}} {dx} \\ $$$$=\int_{\mathrm{0}} ^{\:{t}} {ie}^{{i}\pi{x}} {dx} \\ $$$$ \\ $$$$\left(\mathrm{1}\right) \\ $$$$={i}\int_{\mathrm{0}} ^{\:{t}}…
Question Number 7008 by Tawakalitu. last updated on 05/Aug/16 $${Factorize}:\:\:\left({a}\:−\:{b}\right)^{\mathrm{5}} \:+\:\left({b}\:−\:{c}\right)^{\mathrm{5}} \:+\:\left({c}−\:{a}\right)^{\mathrm{5}} \\ $$ Commented by Yozzii last updated on 05/Aug/16 $$\left({a}−{b}\right),\:\left({b}−{c}\right)\:{and}\:\left({c}−{a}\right)\:{are}\:{factors} \\ $$$${since}\:{the}\:{expression}\:{above}\:{reduces} \\…